Continuous cellulose fiber-reinforced cellulose ester composites III. Commercial matrix and fiber options

Thermoplastic composites were prepared using two continuous regenerated cellulose fiber types, rayon and lyocell, and with several different commercially-available thermoplastic cellulose esters as matrix. Matrix options included cellulose acetate propionate (CAP), and several cellulose acetate butyrates (CAB) with different butyryl content, having different molecular weights and different methods of plasticization (adipates and very low molecular weight cellulose ester fractions). Choice of cellulose ester type was generally found to have little or no effect on mechanical properties. A significant effect, however, was revealed for fiber type. The lyocell-based composites thereby were reflective of the greater stiffness of a fiber produced from anisotropic solution state. Their modulus consistently exceeded 20GPa whereas the rayon fiber-based composites had moduli between 6 and 8GPa. The latter, however, possessed failure strains that were 3 to 4 times greater than their stiffer counterparts.     

Electrostatic sums for polymer chains

A rapidly convergent expression is given for calculating the Madelung energy of infinite linear polymers with small radius.Dedicated to Professor J. Koutecký on the occasion of his 65th birthday     

Complex temperature plane zeros in the mean-field approximation

We derive asymptotic expressions for the complex temperature plane zeros of the infinite-range Ising model in the scaling regime. The results also apply to high-dimensional, short-range Ising systems. For thenth zero in a system ofN spins, the leading asymptotic result ist _n (n/N)^1/2(–1 ±i).     

Symmetries of certain double integrals related to Hall effect devices

The Ramanujan Journal - One encounters iterated elliptic integrals in the study of Hall effect devices, as a result of conformal mappings of Schwarz–Christoffel type. Some of these double...     

Exchange energy for two closed shells generated by a bare Coulomb potential energy −<Emphasis Type="Italic">Ze</Emphasis><Superscript>2</Superscript>/<Emphasis Type="Italic">r</Emphasis> in the limit of large <Emphasis Type="Italic">Z</Emphasis>, in two dimensions

Two-dimensional (2D) inhomogeneous electron assemblies are becoming increasingly important in Condensed Matter and associated technologies. Here, therefore, we contribute to the Density Functional Theory of such 2D electronic systems by calculating, analytically, (i) the idempotent Dirac density matrix γ(r, r′) generated by two closed shells for the bare Coulomb potential −Ze ²/r and (ii) the exchange energy density e_x(r){\varepsilon_x({\bf r})} . Some progress is also possible concerning the exchange potential V _x (r), one non-local approximation being the Slater potential 2e_x(r)/n(r){2\varepsilon_x(r)/n(r)} , with n(r) the ground state electron density. However, to complete the theory of V _x (r), the functional derivative of the single-particle kinetic energy per unit area δt(s)/δn(r) is still required.     

Volume-based thermodynamics: estimations for 2:2 salts

The lattice energy of an ionic crystal, U(POT), can be expressed as a linear function of the inverse cube root of its formula unit volume (i.e., Vm(-1/3)); thus, U(POT) approximately 2I(alpha/Vm(1/3) + beta), where alpha and beta are fitted constants and I is the readily calculated ionic strength factor of the lattice. The standard entropy, S, is a linear function of Vm itself: S approximately kVm + c, with fitted constants k and c. The constants alpha and beta have previously been evaluated for salts with charge ratios of 1:1, 1:2, and 2:1 and for the general case q:p, while values of k and c applicable to ionic solids generally have earlier been reported. In this paper, we obtain alpha and beta, k and c, specifically for 2:2 salts (by studying the ionic oxides, sulfates, and carbonates), finding that U(POT)[MX 2:2]/(kJ mol(-1)) approximately 8(119/Vm(1/3) + 60) and S degree [MX 2:2]/(J K(-1) mol(-1)) approximately 1382V(m) + 16.     

A note on the Moll–Arias de Reyna integral

The Ramanujan Journal - The Moll–Arias de Reyna integral $$\begin{aligned} \int _0^{\infty }\frac{\mathrm{d}x}{(x^2+1)^{3/2}}\frac{1}{\sqrt{\varphi (x)+\sqrt{\varphi (x)}}} \quad \text {...     

Novel cellulose derivatives. IV. Preparation and thermal analysis of waxy esters of cellulose

Cellulose esters with linear aliphatic acyl substituents ranging in size from C₁₂ (lauric acid) to C₂₀ (eicosanoic acid) were prepared in homogeneous solution (DMAc/LiCl) using a novel synthetic method based on the use of a mixed p-toluenesulfonic/carboxylic acid anhydride. The resulting waxy cellulose esters had a high degree of substitution (DS), between 2.8 and 2.9, and showed little degradation. Thermal analysis of these cellulose derivatives by differential scanning calorimetry (DSC) and dynamic mechanical thermal analysis (DMTA) revealed a series of transitions that represented motion by both ester substituents and cellulosic main chain. Broad crystallization and melting transitions attributed to side-chain crystallinity were observed in the range between −19 and +55°C; these side-chain T_m and T_c transition temperatures increased by 10°C per carbon atom of the ester substituent. The T_g of these derivatives increased linearly with increasing substituent size from 94°C for C₁₂ (cellulose laurate) to 134°C for C₂₀ (cellulose eicosanoate). Evidence of “main-chain” crystallization was not observed for these samples, except in the case of peracetylated C₁₂ and C₁₄ esters, which had T_m values of 96°C and 107°C, respectively. © 1996 John Wiley & Sons, Inc.     

Continuous cellulose fiber-reinforced cellulose ester composites. I. Manufacturing options

Thermoplastic fiber composites were prepared using high modulus lyocell (regenerated cellulose) fibers for reinforcement and cellulose acetate butyrate (CAB) as matrix. Choices were made with regard to fiber options (fabric versus continuous tow) and method of matrix deposition (prepregging by powder coating, film stacking, or solution impregnating). The results suggest that solution-prepregged fiber tow consolidated at circa 200°C produced unidirectional consolidated panels with tensile strength, modulus, and strain at failure values of approximately 250MPa,>20GPa and 3–4%, respectively, at fiber volume contents of approximately 60%. Modulus and ultimate tensile strength increased with fiber content, and modulus followed rule-of-mixture behavior. Adequate surface wetting and matrix-fiber adhesion were found with solution-prepregged composites. The unexpectedly low strain at failure (2 to <4%) was attributed to brittle matrix failure, and failure surfaces revealed that the fibers, for the most part, remained intact after the matrix had failed.